CAT 2019 Slot 1

Instructions

For the following questions answer them individually

Question 91

Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is

Video Solution
Question 92

If m and n are integers such that $$(\surd2)^{19} 3^4 4^2 9^m 8^n = 3^n 16^m (\sqrt[4]{64})$$ then m is

Video Solution
Question 93

Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?

Backspace
789
456
123
0.-
Clear All
Video Solution
Question 94

Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is

Video Solution
Question 95

Let x and y be positive real numbers such that
$$\log_{5}{(x + y)} + \log_{5}{(x - y)} = 3,$$ and $$\log_{2}{y} - \log_{2}{x} = 1 - \log_{2}{3}$$. Then $$xy$$ equals

Video Solution
Question 96

Let S be the set of all points (x, y) in the x-y plane such that $$\mid x \mid + \mid y \mid \leq 2$$ and $$\mid x \mid \geq 1.$$ Then, the area, in square units, of the region represented by S equals

Backspace
789
456
123
0.-
Clear All
Video Solution
Question 97

With rectangular axes of coordinates, the number of paths from (1, 1) to (8, 10) via (4, 6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), is

Backspace
789
456
123
0.-
Clear All
Video Solution
Question 98

If the rectangular faces of a brick have their diagonals in the ratio $$3 : 2 \surd3 : \surd{15}$$, then the ratio of the length of the shortest edge of the brick to that of its longest edge is

Video Solution
Question 99

The number of solutions to the equation $$\mid x \mid (6x^2 + 1) = 5x^2$$ is

Backspace
789
456
123
0.-
Clear All
Video Solution
Question 100

Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is

Backspace
789
456
123
0.-
Clear All
Video Solution

Register with

OR
cracku

Boost your Prep!

Download App